Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties
arXiv:1310.4977
Abstract
We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors. When the functions in the TP-RKHS are defined on the Cartesian product of finite discrete sets, in particular, our main problem formulation admits as a special case existing tensor completion problems. Other special cases include transfer learning with multimodal side information and multilinear multitask learning. For the latter case, our kernel-based view is instrumental to derive nonlinear extensions of existing model classes. We give a novel algorithm and show in experiments the usefulness of the proposed extensions.
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Cited by in corpus (5)
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- Efficient Structure-preserving Support Tensor Train Machine
- Bayesian Nonlinear Tensor Regression with Functional Fused Elastic Net Prior
- Dimension-free convergence rates for gradient Langevin dynamics in RKHS
- Provable Adaptation across Multiway Domains via Representation Learning